TY - JOUR

T1 - Design of the inverse function delayed neural network for solving combinatorial optimization problems

AU - Hayakawa, Yoshihiro

AU - Nakajima, Koji

N1 - Funding Information:
Manuscript received May 20, 2008; revised May 19, 2009; accepted October 10, 2009. First published December 11, 2009; current version published February 05, 2010. This work was supported by Japan Society for the Promotion of Sciences, the Grant-in-Aid for Scientific Research.

PY - 2010/2

Y1 - 2010/2

N2 - We have already proposed the inverse function delayed (ID) model as a novel neuron model. The ID model has a negative resistance similar to Bonhoeffervan der Pol (BVP) model and the network has an energy function similar to Hopfield model. The neural network having an energy can converge on a solution of the combinatorial optimization problem and the computation is in parallel and hence fast. However, the existence of local minima is a serious problem. The negative resistance of the ID model can make the network state free from such local minima by selective destabilization. Hence, we expect that it has a potential to overcome the local minimum problems. In computer simulations, we have already shown that the ID network can be free from local minima and that it converges on the optimal solutions. However, the theoretical analysis has not been presented yet. In this paper, we redefine three types of constraints for the particular problems, then we analytically estimate the appropriate network parameters giving the global minimum states only. Moreover, we demonstrate the validity of estimated network parameters by computer simulations.

AB - We have already proposed the inverse function delayed (ID) model as a novel neuron model. The ID model has a negative resistance similar to Bonhoeffervan der Pol (BVP) model and the network has an energy function similar to Hopfield model. The neural network having an energy can converge on a solution of the combinatorial optimization problem and the computation is in parallel and hence fast. However, the existence of local minima is a serious problem. The negative resistance of the ID model can make the network state free from such local minima by selective destabilization. Hence, we expect that it has a potential to overcome the local minimum problems. In computer simulations, we have already shown that the ID network can be free from local minima and that it converges on the optimal solutions. However, the theoretical analysis has not been presented yet. In this paper, we redefine three types of constraints for the particular problems, then we analytically estimate the appropriate network parameters giving the global minimum states only. Moreover, we demonstrate the validity of estimated network parameters by computer simulations.

KW - Combinatorial optimization problem

KW - Negative resistance

KW - Neural network

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U2 - 10.1109/TNN.2009.2035618

DO - 10.1109/TNN.2009.2035618

M3 - Article

C2 - 20007029

AN - SCOPUS:76749145080

VL - 21

SP - 224

EP - 237

JO - IEEE Transactions on Neural Networks and Learning Systems

JF - IEEE Transactions on Neural Networks and Learning Systems

SN - 2162-237X

IS - 2

M1 - 5352267

ER -